For this achievement you must defeat a drake, wyrm, and wyvern.
Defeating the Drake:
The Drake can be found in near Lake Hardship, south of The Shadow Fort at any time in the game. Post game it can be found in Conqueror's Sanctuary, north of Bloodwater Beach in that open area where the Cyclops used to be. It can also be found post game at the Miner's Hut west of Gran Soren. Your last option is the Chamber of Fate in the Everfall. Use this map for help with locations.
For tactics on how to defeat the Drake and other useful information, go here.
Defeating the Wyrm:
The Wyrm can only be found post game. Your options are the Chamber of Distress in the Everfall or The Watergod's Altar. Use this map for help with locations.
For tactics and other useful information, see here.
Defeating the Wyvern
The Wyvern can only be found post game. Two of them can be found at Gran Soren's southern gate during nightfall. You can also find one in between Gran Soren and Windbluff Tower. It will fly off and you will have to follow it. Another can be found at Bluemoon Tower. Use this map for help with locations.
For tactics and other useful information, go here.